• 충청수학회지
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• 제27권3호
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• pp.393-401
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• 2014

In this work, we discuss the existence of mild solutions in the ${\alpha}$-norm for some partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

• 대한수학회지
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• 제55권5호
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• pp.1269-1283
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• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• 충청수학회지
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• 제27권1호
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• pp.89-97
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• 2014

We study the existence of mild solutions for neutral differential equations with nonlocal conditions in the ${\alpha}$-norm.